I think MGS1 is an excellent game, but in my opinion the subsequent games improved on the formula massively. MGS2 had a very similar vibe, and yes whilst I'd agree that some of the bosses can be frustrating, it felt like they were trying to do weird and interesting things (like defusing bombs whilst fighting fatman, and taking out a huge number of metal gears in a single fight). MGS3 just feels like the complete package to me: the best bosses in the series, an incredible soundtrack and a mostly standalone, well written story.
One thing I missed in MGS3 was sneaking around in tight interior spaces. The tanker sequence in MGS2 is a highlight of the series for me - going unnoticed in this heavily guarded ship with the rain streaming down the windows with that jazzy soundtrack playing.
I'm struggling to think of many games that capture the vibe of MGS1. The early Resident Evil games perhaps spring to mind - trying to survive alone with limited ammo and a conspiratorial backstory.
That's true, but there was also a lot of backtracking in MGS1.
I did like the cold, metallic atmosphere of MGS1 with beautiful dithered textures. Likewise, the cell-shaded, organic design of the Big Shell is so nice. Each Metal Gear game seems to have such a unique style.