jiju1943,
I have restored exactly one old pontoon boat, so my experience is limited, but here's my opinion. I removed everything from the deck and then went to remove the original carpet. The old glue held well and it was very, very difficult to get the carpet off. There were numerous places where bits of the old carpet and glue remained well adhered to the wood deck. .... My research indicated some people had tried various power tool implements (e.g., wire brush on drill) in an attempt to remove the old glue. I quickly discovered that it would have taken many, many hours of tedious work to remove what remained behind. As the majority of the deck is covered by furniture, I left those areas as is. I spent a little time on the walking areas knocking down the high spots in the old glue and carpet. I then glued new marine carpet down. There are no noticeable bumps and I'm satisfied with the finished product.
I thought of and decided against vinyl out of fear it would be slick when wet and hot on bare feet when dry. It would have also required me to do a much better and more time consuming job preparing the deck. Vinyl shows what's beneath far more than carpet. If I had to do it again, I'd again use marine carpet.