I have both a Bitaxe and an S9, so I can give you some insight here.

If you plan to use the heat generated by the S9, go that direction. If not, go with the Bitaxe. Yes, they are about the same price up-front, but the S9 is going to use WAY more power per TH than the Bitaxe. Efficiency is important, and it's why the Bitaxe doesn't cost 1/10 of the price of the S9, despite producing less than 1/10 of the hashrate.

An S9 can get you 13.5-14 TH of raw hashing power, but it's efficiency is only 0.1 joules per gigahash. Compare that to a Bitaxe Gamma, which is only about 1.2 TH, but does so at an efficiency of merely 0.01 joules per gigahash.

Then you have sound pollution to take into account when talking about home mining. The default fans on the S9 are LOUD. You will need to do something to mitigate that if you want to live peaceably with anyone else in your household. Even if you replace them with quieter fans, though, it's still pretty noticeably loud when running at full power. Most folks using S9s as space heaters are running them at half power, and they are not bad volume there, but then you are getting even worse efficiency and less overall hashrate.

Also, keep in mind that you probably aren't going to be profitable, even with a Bitaxe, unless you have really cheap power. Consider it a hobby and something you are doing to learn more about how Bitcoin works, and get some KYC sats at a bit of a premium cost. Of course, you might also go the lottery mining route, where you don't make any sats at all unless you are fortunate enough to find a block. That is always an option, too.