I am going to start using my big swimbaits and Alabama rigs a lot more. I am trying to decide whether I should buy the Daiwa Millionaire S reel or the Lews Laser MG Speed Spool. which do y'all think would be better & why? thanks in advance!

Get the best reel you can afford. ARigs and big swimbaits put a hurting on equipment. Think of towing a boat with a vehicle. You wanna tow with a Mini Cooper or a Super Duty F350?

I toss my bigger baits with a Diawa Advantage HSTA. I throw nothing over 1.75oz and its a chore for that reel. Round reels will be better IMO. Cardiffs, Calcutta, Luna. Atleast 200 size for holding good quantity of bigger line.

You want at least a 300 series reel. Smaller reels with grenade if you are throwing big baits. I throw my swimbaits on Calcutta 400's and Curado 300's.

Cardiff 300, Abu 5500 C3, Lexa 300, Curado 300, and Abu Toro are all beasts that can handle up to ~4oz.

I am going to start using my big swimbaits and Alabama rigs a lot more. I am trying to decide whether I should buy the Daiwa Millionaire S reel or the Lews Laser MG Speed Spool. which do y'all think would be better & why? thanks in advance!

I really like Lews reels. 

You want at least a 300 series reel. Smaller reels with grenade if you are throwing big baits. I throw my swimbaits on Calcutta 400's and Curado 300's.

 

This.

 

Or a Cardiff if you don't want to spend a lot. I have a few Cardiffs and they have served me well.

I throw most of my big baits on a Curado 300 and couldn't be happier with it. I've handled fish up to 20lbs (striper) on it without an issue. If I'm tossing really big baits then I'll switch to my 400 Calcutta. The Cardiff is a good, affordable reel that will get the job done as well.

I get good results with my older pflueger trion. I do worry about them wearing out soon, however.

The Trion holds quite a bit of 25# flouro for tossing my big swim baits and Arigs.

I absolutely hate round reels. They are great pieces of machinery but I just hate how they sit in my hand. That is why I throw my a-rig/ swimbaits on my revo winch. It has enough power to get it done. If I want to get a dedicated heavy a rig and swimbait reel then I will buy a revo toro winch or similar reel. Even the Curado 300 will work.   

I use a Curado 301E for all my A-rig & big swimbait fishing and love the thing. It's a tank, plenty of drag and cranking power for these techniques. I use 25# P-Line CXX on mine and it holds more than enough. Can't recommend this reel enough.