Working with mains voltages is always a safety hazard if improperly handled. In both examples, you have 240 V AC effectively present on the PCB or wherever the relay is mounted. It should be designed with proper clearances, labeling, and safety guards and so forth. (Even if it's a one-off hobby project, I always would make sure to insulate and label so that future me or anyone else is well-aware.)
In both examples, the load is on the neutral line, so when the relay is switched off someone could interact with the load and be safe. (I would still open the mains breaker before touching any part of this.)
Also in both examples, if the DC voltage to the relay fails or is interrupted, the way you've connected them, it would open the AC side and therefore is somewhat of a fail safe (it fails to safe mode).
Something to consider is that when switches open and close, there is always a bit of arcing. The relay must be rated for the correct current and voltage. You may note that relays will be rated for a different voltage and current for AC versus DC, and this is because there is a zero-crossing with AC, which allows the contacts an opportunity to open. In a worst-case scenario, say with too much current, the contacts might "stick". It's possible, therefore, to switch off the coil side of the relay but the switched side doesn't switch. Again, this is "worst case" and is unlikely to occur as long as everything is rated for the appropriate load.
Personally, I find both options functionally equivalent, but if for some reason I wanted to alternate between two loads, I would prefer to have the live line connected to the relay common - and because of this, I think it more conventional. Thus option 1 is my preference, but I don't think there's much to say beyond this being a preference.