One way or another, you are going to experience the difficulty of the market.
When a market is up, there are usually more buyers than sellers. That's what's driving the price up. This shows in how quickly a fairly priced property will sell. As a seller, this is fun. You often get the price you ask for, sometimes even more, and you sell quickly. But if you need to turn around and buy a place in this same market, you get to experience the crappy part. You are competing with all the other buyers, so you get the stress of having to check listing sites multiple times per day because places are moving that fast. And when you find a place you like, you call and get the disheartening news that they already have 8 offers, it's been bid up, so if you're not paying cash you can piss off.
This is all basically reversed if you sell/buy when the market is down. You'll really hate the selling part, probably not get the price you want, have few offers, and it'll take longer than you hoped. As a buyer, you'll have tons of time and options. It'll be downright fun.
The only way to have your cake and eat it to is to sell when the market is up, rent or move in with mom and dad, then buy when the market is down. But renting or moving in with the parents for 6 to 18 months is not really my idea of good cake.
Inasmuch as the actual numbers if you buy/sell at the same time, if the prices are fair, you are essentially just moving equity to a different property. You'll find that it's pretty close to even when all is said and done.