The quick answer is that he would most likely wear neither. He would wear armour that was in fashion in England, not in German lands or in Northern Italy. This might be a 'native' English armour, or an Italian-made 'export' armour, or an armour from the low countries made in the style popular in Northwestern Europe, or maybe an armour in a style popular in France. But it is exceedingly unlikely that a man at arms from from Lancashire would wear the same armour as a man at arms from Pavia or Hesse - even if he was wearing an armour that was made in Milan!

The long answer is much more interesting. I have adapted this from some previous answers. First, let's talk about the premise that the two armour styles of the later 15th century are 'gothic' and 'Italian' (or Milanese) and that 15th century armours are one or the other. This requires a bit of a digression on the historiography of armour and the nature of armour scholarship. Traditionally, armour history is art history, and much of the scholarship revolves are cataloging, describing, classifying and (hopefully) contextualizing extant pieces. Extant 15th century armour is rare. Much of what survives, and all of the complete harnesses that survive, are either made in Southern Germany or Northern Italy - the area betwen Nurnberg and Milan. In part this reflects the importance of these places as manufacturing centers in the period (Nurnberg and especially Milan were -massive- production centers), but in part it is a fluke of history - Cologne in northwestern Germany was a massive producer of armour, yet little survives from there, and regionally important centers like London have no armour surviving. Moreover, while Milan was the greatest armouring center in Europe, not all armours made in 'Milan' looked like what we would think of as 'Milanese' armour - the Milanese armourers were incredibly adaptable businessmen and made armour to the local tastes. And while some of these Milanese 'export' armours survive, many of the surviving pieces are from a few sites within Italy itself (particularly the Castle Churburg and a church in Mantua), which means that 'native' Italian armours are over-represented among survivals, compared to the exports that once flooded the European market. So the survival bias of armour has divided the world of 15th century armour perhaps too starkly between German 'Gothic' armour and 'Milanese' armour. Also, a word on 'gothic' armour - this is not a medieval term, since 'gothic' wouldn't be applied to architecture until the Renaissance, and the term wasn't applied to armour until the 19th century. Moreover, 'gothic' armour was only in vogue for a brief period - around 1460 to 1490 or so. Moreover, there is little evidence that this style of armour was exported outside of the holy Roman Empire and points to the north and east of it (Scandinavia wore a kind of north german style armour, while Polish or Hungarian armours resemble those made in Nurnberg - probably because that is where they were made!). However, a number of armours from central and southern Germany survive from this period, and the style's distinctive appearance gave it a lot of appeal when national romanticism became popular in the later 19th century - it was seen as distinctively 'German'. So our ideas about 'Gothic' and 'Milanese armour are affected greatly by the armour that survives and by the agendas of previous historians.

In fact, every nation in Europe had its own stylistic foibles. Some of these were shared across broad geographic areas - there are characteristics of armour that are seen from the low countries to Portugal, while others are weirdly discontinuous, where some characteristic form of armour will show up on nearly opposite sides of Europe at the same time. At the same time the armours of countries might not even resemble those of their neighbors - English and French armours are often quite different, as are those of the Flemish lands and central Germany, not so far away. Moreover, different styles of armour coexisted side-by-side in the same country - in German lands you can see both 'native' armours and Italian export armours made in the German fashion ('Alla Tedesca'). To put it another way, the style of armour was a matter of fashion, and people wore what was in fashion in their country. But it wasn't just fashion. Armour was also practical protection, and it was adapted to the way that its wearers fought. So, for instance, Italian armours, made for Italian men at arms fighting on horseback with a lance, have heavy reinforcements against lance strikes (so that almost the entire front of the armour has double layers of steel) and less concern about weight or movement of both arms far over the head. By contrast English armours, which were made for men at arms who often fought on foot, have long skirts, closed cuisses (thigh armours) and maneuverable shoulder defenses to make it easier and safer to fight on foot with a two-handed weapon. So from a certain perspective, there are as many styles of armour in Europe as you can care to name, sometimes more than one in a single country at a single time!

Speaking more broadly, the question 'does this regional peculiarity make for a distinctive style' is one of terminology - how do we define 'style'? What is a superficial difference, and what is a different style entirely? The great armour historian Claude Blair looked a a number of underlying structural differences (particularly the construction of the arm harness) to define distinctive 'German' and 'Italian' construction methods that persist from the later 14th century to the early 16th. But in all honesty given that the rest of Europe follows an 'Italian' construction for the arm harness we might define that as 'German' and 'everything else.'

But while this underlying construction difference is persistent and illustrative, is it all that matters? Clearly not. We can also look at the structure of the pauldrons, the form of the gauntlets, the length of the fauld/culet, the type of helmet - really any aspect of an armour - when we talk about its style. And when we look at it we do see some persistent preferences in the armours of different nations, but we also see quit a bit of overlap, borrowing and convergence. So let's leave aside the terminological question of 'style' and ask - did different armours from different armourers across Europe look different? Did armours made for customers in different parts of Europe look different? Yes, they did.

Generally the different nations of Europe had their own stylistic preferences and their own particular favorite times of gauntlets and helmets etc. For instance, the 'close helm' closure system, where the bevor and visor pivot from a single point (rather than the bevor being strapped in) probably originates in the low countries an spreads to the rest of Europe at the end of the 15th century; based on surviving depictions low country armourers are also some of the first to move back to a one-piece breastplate, rather than a two-piece breastplate that includes a plackart. I talk a lot more about low countries armour here. For France, the style seems to follow Italian 'export' armours, as far as I can tell, but the French are among the first nations to adopt the sallet and bevor as the primary knightly helmet - based on manuscript illustrations they were wearing them in great numbers at a time when their neighbors in England and the Holy Roman Empire were still wearing great bascinets. Mind you, this applies to the 15th century, which is generally the period people are talking about when they speak of distinctively national armour styles.

Thus in the 15th century in addition to German and Italian styles you have regional styles in much of Western Europe, such as England, the Low Countries, France and Spain.

How do we study these without extant examples? Fortunately we do have pictorial and sculptural sources. Some of these (mostly English Funerary Effigies and Neatherlandish paintings) can be good sources if they are interpreted correctly. So we can get a good idea of what the armour -looked- like.