In general android phones are more finicky. And its easier to buy a dog unless you exactly what you are looking for. I phone you know exactly what you are getting. A GOOD Android handset is the equal of an I phone , in fact better in some areas. But you need AT LEAST 16GB on board storage and 2GB of RAM coupled with a decent processor if you want the latest version of Android to run smoothly.
Apple phones also lag, the older versions are more likely.
Lag apn all phones is due a few items, as Kippies said memory is the greatest issue, cheap phones with 1GB RAM or less will all lag, 2GB or RAM may lag if its multi tasking at the time, or that you've loaded the on board storage above 75% of capacity.
Phones with quad core processors or larger with larger than 2 GB for RAM and large qty of on board storage, will normally not suffer from lag until the storage is getting full, so 2 GB RAM and 32 GB of storage is a great place to start along with a decent quad core or larger CPU.
Removable storage is great if you can get it ( not avail on all Apple phones, newer Samsung and others) as you can swop out to larger storage cards as you need to (and prices always go down as bigger and faster memory cards become available.
What you should have picked up by now is that you should buy a decently spec' device to get decent performance, you get what you pay for and don't forget to do your research as on occasions high priced stuff can still be a dog recent Sony phones are a good example of that