Unfortunately I can't compare it to Mediterranean sea travel, but I can talk about how the cost of pilgrimage in late medieval England and potentially someone else could chime in on sea travel!

Pilgrimage as a whole became almost like a package holiday between 1100-1500, especially with affective piety being in vogue (affective piety is the focus on Christ as a human and his experiences, which made Christians want to experience the places he had been through pilgrimage in imitatio Christi). By the 1300s there were well established tours and routes to the main places of pilgrimage (Rome, Santiago de Compestela, and Jerusalem). Between 1100 and 1500 there were around 526 accounts of pilgrimage written, many would have been in local circulations was well, and by the early 1400s there were guidebooks telling pilgrims exactly where to sleep, eat, how to change money, were crime was, etc. Alongside it being a religious experience for some pilgrims, others used pilgrimage as a way to see the world and travel.

Despite this, pilgrimage was extremely expensive and arduous during the medieval period. To begin with, before you even left you would have to settle any and all debts before leaving, as well as make up your will before leaving. Then you have the cost of travel itself, which could easily cost the entire years salary for someone in the merchant class. For example, a return journey from Venice to Jaffa for the Jerusalem pilgrimage would cost around 15 pounds, compared to a carpenters wage for the year which was 12 pounds. But to even get to Venice you have to spend more to travel from England, for example travelling by sea to Zealand in the Netherlands and then through the Alps to Venice. Then on top of that you have to pay food and board for the journey, as well as have extra money if you wanted a souvenir like a pilgrim badge to show off your piety. Margery Kempe is arguably one of the most well known accounts of pilgrimage in medieval England and it is estimated she brought 36 pounds of cash with her for her pilgrimage to Jerusalem in 1413 following this route, which would have allowed her a comfortable pilgrimage.

For your example, the pilgrimage to Rome could take up to sixteen weeks overland from Calais. So we have the cost of travelling to Calais, plus the additional costs I've mentioned such as food and board over sixteen weeks, and the debt-settling too.

Hope this helps a bit!