I haven't owned that particular Seiko, but I've handled the SLA043 extensively and I owned the blue version of the FXD for a few months last year.
The Tudor is fantastic - amazing titanium case, movement kept terrific time (better than my Rolexes), and the legibility was amazing. But I found the case to be a tad big for my wrists (6.75") and I found the dial to be quite shallow and lacking depth. The SLA043 fit much better on my wrist, had a much more interesting and visually pleasing dial (to me) and the movement performed reasonable well for a Seiko. The SLA037 has a different movement compared to the SLA043, so your mileage may vary with that.
If I was in your position trying to pick between these two, I think I would go for the SLA037.
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