I bought the Irix 150mm sometime early last year and, given that I feel we're just getting acquainted, I was surprised to find out that I must have taken close to 1000 pictures with it already. The Laowa only arrived on Dec 24th, so it hasn't seen a 'macro season' yet.
In addition to the obvious differences that tryphon4 and bdery listed, handling feels somewhat different.
The Irix is easier to focus than the LAOWA. One reason is that, while both lenses are labelled f/2.8, the Laowa is at least 1/2 stop darker than the Irix. The difference is a lot more pronounced at 1:1, where the Irix surpasses the otherwise leading DFA100WR (surprising, I know, with it's small front lens). I may post some measurements later, but the difference is obvious in the viewfinder, and I did reach out to the Irix in the evening hours over the DFA because of the brighter viewfinder image. The other reason is the very short focus throw of the Laowa, covering the huge range within ~ 120 degrees. The Irix is similar to the DFA100WR, the larger diameter is offset by higher friction/damping. Scales on the Laowa are cramped and not well labelled, the ones on the Irix are much more usable - on par again with the DFA100WR, where I would wish for a denser distance scale to make the DoF markers more usable. The Irix doesn't have any, the ones on the Laowa are plain wrong by a huge factor.
Despite the Irix rendering and bright viewfinder advantage, the DFA100WR got preference on a couple of macro shots last year, because I didn't have a standard lighting setup yet - it's harder to do with the Irix. If you use the hood on the Irix, the working distance becomes small and light angles steep. But you need to avoid light on the rather exposed front lens. The Laowa at 1:1 should work well without the hard to attach hood if you don't need the front protective filter, which seals off the otherwise exposed innards. With the hood, working distance is again fairly small. The plane filter may not be a problem flare-wise - yet to be seen and potentially can be improved by a different filter. At 2:1, the front lens is finally at the front - but then none of the others does 2:1 natively.
The lens-side of the hood bayonet seems to be plastic on the Irix and aluminum on the Laowa. It does make a difference to me: I have worn out the lens side of my first DA18-135mm in about 5 years by reversing the hood for storage in my bag. Also a new hood didn't stay on reliably! I'm very careful since, stowing my lenses with the hood on whenever I have enough room, but the metal bayonet promises better abrasion resistance in the long term. I do consider lenses to be used for a long time, even if not by me personally.
The Irix's diameter is too big to mount my ring flash, which I like to use as fill light sometimes (esp. bottom half), using the supplied rings/plates. For the Laowa, I don't feel I need to go through the hoops of attaching it to a spare hood as I did for the DFA100WR in the same fashion as the Pentax AF160FC does, because the filter thread is on the robust outer barrel, so it works as designed just screwing in the flash mount plate. For the Irix, I need to get a similar step-down-and-up again stack of rings as I glued into the spare DFA hood. The open diameter will still be larger than the front lens. Doable, but not as convenient. Btw., I lLOVE the tightly fitting, very well made Irix case, which makes it easy to throw it into my backpacks. The Irix comes with a well designed tripod foot. I don't the Laowa one yet, but will order one mainly for balance with the ring flash head. Otherwise balance is not really an issue - not even close to the DFA15-30mm/2.8, for which there is none.
Image quality wise, there are some opinions already. From the little use it has seen so far, the Laowa looks as nice as the Irix, if not a hair better at macro distances. Apochromatic correction seems to be even better than the Irix's (visible mainly wide open) - but both are really close and significantly better than the DFA100WR.. From a rendering perspective, I don't have enough examples to thoroughly compare them yet but what I've seen so far, it's again a close call with the Laowa having a slight edge in smoothness of both the foreground and background - at 1:1.
In conclusion, you can't go wrong with either and I would consider the Laowa a bit more complementary to the DFA100WR than the Irix in terms of macro use, the Irix however in terms of non-macro use.