I am in a bit of a quandary. I have Luepold bases and rings (1") currently on my rifle. I bought a new 30mm scope which requires new rings obviously. I read about 1 piece bases and Weaver style rings and wonder if one system is better than the other in reality. To me the Luepold seems stronger since it is more or less anchored on the front, but all the target guys seem to go with Weaver style mounts, Is there a fundamental right or wrong to either style? This is a hunting rifle in one sense but on the other hand it will be wearing a EPB reticle scope. I appreciate the input

GO with Tally ring. Best you can get.

I know there is better but.... I use standard Leupold I have 1" and 30mm both.

X's 2 We love Talley. I haven't seen anyone who has more user specific mounts.
The only way to go with hunting rifles.

For the money and hunting....Talley.

For the best with a little overkill, Nightforce base w/ N.F. Ultralight rings.

Just my opinion though.

It depends on rifle and how big it is doesn't it. The one piece base in theory would be more rigid and help with recoil. Let me know if I'm way off base

That's somewhat true. A pic rail is also going to allow for more adjustment back and forth for your correct eye relief. And a canted base is also going to benefit you in putting lead down, down, down range. A 20 minute base will compensate for this.
For optics that do not have enough internal adjustment to put you where you want to be. I have customers put Talley's a .338 and many of you know how abusive the recoil is on that.
Like with Badger Ordinance with their steel bases and rings.
They are rock solid, but mostly seen on tactical rifles and long range shooters.

Then there are some who use their LR rifle to hunt with as well.

Just depends on how you plan to use your weapon.

But like I said earlier, Talley is really the way to go. You will not be dis-appointed.

I am shocked Warne was not mentioned. Same design as Talley, in some cases almost half the price. I have never seen an issue with any of there products.. fixed, tactical or QD. The QD and tactical have always repeated poi if assembled correctly on a one piece base like EGW at the lower end to Ken Farrel or USoptics, Night Force etc... on the other end.

Cha-ching .02