I've started pondering on this topic after seeing that, contrary to my predictions, Fate tends to be by far the most precious resource, whereas Honor is not as much of concern unless you're playing Lion, and Cards are usually quite abundant.
As for the last two, I think the reason for that is that Honor doesn't really matter as long as you have more than 5 and your opponent has less than 20. This means both players will usually draw lots of cards: a player could start bidding low to force their opponent to do the same, but he would have to concede an advantage of 6-8 cards first (since all three Clans previewed so far start at 11 or 12 honor). A 6 cards advantage in the early rounds is truly massive, especially considering how many powerful 0-cost Conflict cards exist (For Shame!, Banzai, Fine Katana just to mention the neutral ones). I've won games with Lions in which I bid 1 for the first 3 rounds, since I had Historians and/or Recruits in my early flops, but I have the feeling having non-"honor dependent" characters and drawing extra cards would've served me much better.
Fate, on the other hand, seems to be a lot more precious than one might think at first. Since you need Fate to 1) pay for characters 2) pay for events/attachments and 3) to have characters stick around, you have basically never enough Fate. So now I'm considering a more "theorethical" question:
How much is a single Fate worth compared to a Conflict Card?
It's safe to say a Conflict Card is worth a 2 Honor difference. The important thing to note here is that when you gain a Honor and when you make your opponent lose one Honor your are actually working towards two different victory conditions: this means that the price for a card during the Draw phase is "split" between those two independent paths, so that it is less pricey than if it were to be, say, a straight 2 Honor gain for your opponent. As a result, cards in the Draw phase are cheaper than what they might appear.
So what about Fate? What Fate does that Conflict Cards do not is buying you characters. The easiest thing to take as reference point for characters is their statistics - of course this means possibly missing the strenght of their abilities, which is not as easy to quantify - so we could try to compare them to Conflict Cards that give bonuses to raw stats. Fine Katana - and Ornate Fan, if speculation is confirmed - seem to be the best cards to consider for this comparison: for the price of 0 Fate 1 CC a character gains a permanent +2 to a Stat. Since Conflict Cards can be played as Actions, it usually means the character will get the bonus for the characterstic that's relevant for the current Conflict, meaning it's more worthwhile than a +1/+1 split between Mil and Pol. Let's compare this to the stats you gain per Fate spent: characters with a cost of 2 or more tend to have stats more or less equal to at most their cost (mostly depending on how strong their ability is considered), i.e. a 2 cost char usually has at most 2 Mil 2 Pol. This means a Katana/Fan would provide a stats increase roughly equivalent to 2 Fate. So the Hypothesis is 2 Fate = 1 CC. Let's also simplify things a bit compared to what I said above and make it 1 CC = 2 Honor; so 1 Honor = 1 Fate. I'll bring a few examples from the cards we know so far that, I think, confirm this equation (keeping in mind, however, that when designing games such things are generally used as guidelines, not as strict equations).
Honored Blade vs Fine Katana: 1 additional Fate, conditionally gain 1 Honor (possibly more, but there is a strict requirement of winning the Conflicts). Check.
Height of Fashion vs Ornate Fan: 2 additonal Fate for +2 Pol = +1 Ornate Fan for an extra 2 Fate => 1 Ornate Fan = 2 Fate => 1 CC = 2 Fate. Check.
Ancestral Daisho (Kitsuki's Method) vs Fine Katana (Ornate Fan): 1 additional Fate to gain 1 card back and 1 additional Fate to replay it => 2 Fate = 1 CC. Check.
So it would seem that, indeed: 2 Fate = 2 Honor = 1 CC. However I think Fate is actually a lot more worthwhile than that. The fact that a single extra Fate put on a character with a cost of 2+, or a character with attachments, essentially gives you a copy of that character for the next round makes it so that 1 Fate is worth a lot more in the long term than it would have if you spent it on something else this round - think about how good Good Omen turned out to be. Since even quick games of L5R take at least 3 rounds, there is always going to be the need for extra Fate to be put on characters. This of course requires a balance between Tempo considerations and long-term ones (I propose the term Momentum as a shorthand), so one cannot say 1 Fate on Yokuni = 5 Fate; however that Fate put on a Clan Champion is surely worth at least 2 Fate, possibly more depending on the situation. Economy cards, i.e. cards that sacrifice the short term for a long term gain, exist in all card games - in this game, the best economy involves keeping your characters around, thus having additional Fate. The fact that Conflict Cards are so cheap to acquire makes, by comparison, Fate even more important.
My conclusion is that we should look at cards that generate/manipulate Fate (or are free to play) with attention, since they might end up being stronger than what they would seem to be on paper, and, conversely, we should probably evaluate cards that are Fate-intensive with additional caution.