Was there less defence? Better docks?
Looking at a modern map, it's hard to imagine why an invasion force would have chosen a featureless spot like Pevensey to land at. We need to look at a map of the coastline as it existed in 1066, before generations of silting, coastal erosion and land reclamation works fundamentally changed the outline of Britain.
There are dramatic differences. The sea - and brackish coastal marshes - reached as far inland as Cambridge; much of Somerset was also an arm of the sea. And Pevensey was a substantial, sheltered bay, as this close-up, with the modern coastline in lighter tone, and the contemporary one in a darker shade, shows.
Source
David Hill, An Atlas of Anglo-Saxon England, 700-1066 (1981)
The generally accepted answer is that there was more room for landing ships that Pevensey, in addition to an old Roman fortification large enough for the entire army to camp in. According to Bernard Bachrach, there may also have been the remnants of a Roman deep water port, which would have allowed the unloading of the larger ships directly onto the docks, rather than cargo and horses being lowered over the side, placed into lighters and then ferried ashore. I've not seen any other authors back this last idea, but it's not impossible, as Pevensey was later one arm of the Cinque Port of Hastings.
However, Christopher Hewitt has recently suggested that Pevensey was not a large bay, but instead "more akin to a large marsh with loosely defined fluvial channels". This is based on the 14th century Gough Map, which doesn't show any bay at Pevensey, as well as late 16th century maps drawn up in anticipation of the Spanish Armada which show the area as marshy. However, this does not mean that Pevensey was not a good choice for a large fleet: it may only have flooded periodically, the tides were lower at the time of year when William arrived and, furthermore, there would have still been plenty of channels and dry areas at the edges where ships could be beached. Small boats, combined with pontoons, could also have been used to cross the channels in the marsh if required, and we know that small boats were used to transport supplies.
The reason why a large bay would be ideal is that William had a lot of ships, and he couldn't know how long he would have to land his forces before considerable opposition was brought against him. It's generally accepted that he had at least 700 larger ships to transport his men and horses, but the total may have exceeded a thousand, without counting the smaller vessels used to transport the supplies. With the widespread deployment of Anglo-Saxon troops prior to William's delays, the speed at which they could move and the quality of the message service, he couldn't afford to take three or four days to unload all his men.
Apart from the Roman fort and the large area on which to land, Pevensey was also the end point for a system of medieval roads that linked up with a Roman road and lead deep into Wessex, where Harold held a considerable amount of land. This would make raiding his lands, destroying Harold's credibility with his people and his economic base, easier, and the Roman roads also offered quicker access to London than the medieval roads leading from Hastings. Pevensey also had multiple mills in close proximity, important for less time consuming production of flour, multiple salt houses, which would have aided in the preservation of meat, and some of the richest land in the south of England was directly west of Pevensey, which would have gone a good way towards providing money to pay William's men.
Why William chose to move most of his forces to Hastings is hard to discern. His strategic plans may have changed, or Pevensey might have proven unsuitable for a large army, either due to lack of accommodation or less food reserves than expected. Hastings likely did have better port facilities, and William might have had a significant number of early cogs and proto-hulcs that Pevensey couldn't handle. Being a larger town, Hastings probably also had more food available for the army and, additionally, it had a small mint which might have provided William with more money to pay his troops.
Honestly, though, this is all speculation. While we have reasonable evidence for road networks, the relative importance of the ports, fiscal value of land and land ownership, we have almost no evidence of William's strategic plans in the lead up to the Battle of Hastings, and none as to why he chose to land at Pevensey over Hastings, or why he then moved to Hastings. Almost no fragments of administrative documents for the Conquest exist, and the remaining evidence comes from chronicles, all of which are biased in one direction or the other, some in verse and others written decades after the events, but still within living memory and drawing on anecdotes and now-lost sources. Interpreting it isn't easy, and everyone has their own version of what they think happened. This is all just my best guess, based on the primary and secondary sources I've read.
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