For lead acid batteries, voltage is good enough for reporting state of charge. Especially if you don't need detailed time information and just want to report "low battery".
It's not exactly linear, but it's close enough: Battery discharge curves
I think you will be disappointed with that battery.
Lead acid batteries are best on low rate discharge. Most these days are rated at 20hrs. That battery is rated 8Ah, so will deliver that capacity when discharged over a 20hr period, at 400mA. At higher currents, the capacity will be less. Here are a few lines taken from the discharge capacity table in the data sheet, for constant current discharge, down to a cell voltage of 1.75v (more of that later!)
current period capacity
0.4A 20Hr 8.0Ah
4.8A 1Hr 4.8Ah
16.5A 10min 2.8Ah
so there's quite a capacity penalty to high rates of discharge.
A 150W inverter will take around 15A (assuming 85% efficiency) to deliver full power, 7A is only around half maximum load.
The lifetime of a lead acid battery, before it wears out, is strongly related to its depth of discharge. That battery rates 260 cycles at 100% DOD, ie to 1.75v. You can double that lifetime if you only discharge to 50%, and x5 if you go to 30%, that is, stop discharge at a higher voltage. Depending on how you want to use it, weight and capacity may be more important than cycle lifetime to you.
It's not clear whether you have a vehicle with you, or everything is carried in your kayak. If you have the capacity to carry more weight, then a cheap auto battery is by far the best bang for buck for the sort of currents you are talking about.
Both nickel and lithium chemistries stand up to high rates of discharge better than lead, and lithium in particular gives a much better power and energy per unit weight.
Best Answer
It sounds like both batteries are likely end of life, but testing them is a great way to determine if there is useable life remaining. I'm assuming that you don't consider the burglar alarm to be mission-critical, as using a marginal battery in applications that really need reliable power is a bad idea.
First, measure the terminal voltage during charging (but after they've been on the charger for at least 24 hours). The terminal voltage should be between 6.0V and 7.5V. If it's less than 6.0V, you have a shorted cell and should recycle the battery; it's done.
Next remove the cell from the charger and measure the terminal voltage. If it is 6.0V or greater, there may be some useful life remaining in the battery. Reference a typical VRLA battery terminal voltage vs SOC curve below (note that this is for a healthy battery).
Finally, connect a load such as a 6V light bulb across the terminals while measuring the terminal voltage. If the battery lights the lamp and the terminal voltage stays above 5.8V or so (assuming a ~500mA load), you're probably OK given the caveats about not using marginal batteries in important applications.