このかた isn't felt older to me, but they do have a little difference in meaning.
Both ～して以来 and ～してこのかた can be translated "since X", but 以来 tend to focus on X, suggesting it is a notable, important turning point, or reference point to explain the story thereafter. In contrast, このかた puts focus on the period after X, that has significance, being long, full of memories, or whatever special, but X itself is usually incidental. In other words, 以来 actually means "Having begun from X, —" while このかた means "In all the time between X and now, —".
thus sounds stiff to me, as this sentence apparently means you start to want to climb that mountain because you saw the picture. The second rewording is natural and almost synonymous.
Usage-wise, it should be noted that このかた is hardly used when telling objective frequency. Even if you said 就職してこのかた三回目, it would only be understood that you wanted to say "three times" is too rare, or too frequent, compared to such a long, or short, duration.
Grammatically, 以来 has a predicative meaning "be the first time since". このかた can never be used as predicate.