I have been a few times (we were very lucky to get free tickets) and have always liked the small, 'artisan' gardens best - some have invariably been enchanting. I never like the very minimalist, hyper modern ones, though this is down to,personal taste, I know.
Last time I went I took a friend who had never been. It was supposed to be a treat for someone who'd been through difficult times, but it was so disappointing. It was chilly, and raining on and off, and we could not find ANYwhere undercover to have lunch. Many people inc. us were sheltering under trees to eat food from stalls. If I had paid for tickets and spent a lot on getting there (neither in our case) I would have been really angry. The organisers KNOW the weather in May is not reliable - why do they not provide more sheltered places to eat? Anywhere we found, there was a 'waiting list' of an hour! And hardly anywhere to get undercover, except the big marquee, which was absolutely heaving with other people wanting to be out of the rain.
Chelsea can be lovely on a good day, but free or not I will never go again - apart from anything else it is invariably terribly crowded. I much prefer Hampton Court - infinitely more space, much the same things, or even more, and in July it's at least a lot less likely to be so chilly. I would choose HC over Chelsea any day.