Hi there. Personally, out of the 2 you have shown us i think the 2nd is the nicer option. Stainless pipes, rack, slightly newer, better colour scheme and the overall condition looks better. Dealers normally overdescribe bikes too in order to attract interested parties and the 1st one is only described as 'good' which probably means 'shit'.
The amount of owners a bike has had is not always an issue if it has been looked after. Some 1 owner bikes i have seen that are only a year old have been in a terrible state and the owners shouldn't have even been allowed a pushbike, let alone a motorbike.
The mileage is also not an issue if the bike has been cared for but like most things mechanical, if it's neglected it will fail sooner or later.
If it were my money and i had £1800 to spend and wanted a mk1 boxeye, i would keep looking and also consider buying privately as i think there are better examples about for the money. Buying privately obviously comes with certain risks as most bikes will be 'sold as seen' and you won't have much comeback if anything goes wrong but if you know what you are looking at or take someone with you who does then you should be fine. My 'R' (1998) plated mk1 boxeye with 15,000 on the clock and pretty damn tidy (if i do say so myself) cost me £1000.
Admittedly, i have spent a few quid giving it a good, clean and service, oil, filters, plugs, rear tyre and the 'slip on' can but it still comes in at well under your budget